<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-28</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001757898</issuerCik>
        <issuerName>STERIS plc</issuerName>
        <issuerTradingSymbol>STE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001413087</rptOwnerCik>
            <rptOwnerName>Rosebrough Walter M Jr</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O 70 SIR JOHN ROGERSON'S QUAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DUBLIN</rptOwnerCity>
            <rptOwnerState>L2</rptOwnerState>
            <rptOwnerZipCode>2</rptOwnerZipCode>
            <rptOwnerStateDescription>IRELAND</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-28</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1685</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>133.92</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>47210</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Ordinary Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>13000</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote Below.</value>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">1,685 shares were withheld from the 3,625 restricted shares that vested on May 28, 2019. These 1,685 ordinary shares represent the value of the taxes required to be withheld pursuant to applicable employment or tax laws, as determined by the Issuer. These 3,625 ordinary shares were awarded to Mr. Rosebrough on August 10, 2015 as part of an award of 14,500 restricted shares. These vested shares were valued at the NYSE closing market price on May 28, 2019.</footnote>
        <footnote id="F2">These 47,210 ordinary shares are held by the reporting person as trustee of a revocable trust established for his benefit. 33,750 of these ordinary shares are restricted. The restrictions on these ordinary shares lapse as follows: 4,000 on May 30, 2019; 3,097 on May 31, 2019; 4,681 on June 3, 2019; 4,681 on June 1, 2020; 4,000 on June 1, 2020; 3,097 on June 1, 2020; 4,000 on June 1, 2021; 3,097 on June 1, 2021 and 3,097 on May 31, 2022.</footnote>
        <footnote id="F3">These ordinary shares are held by the reporting person's spouse as trustee of a revocable trust established for her benefit.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ronald E. Snyder, Authorized Representative under Power of Attorney</signatureName>
        <signatureDate>2019-05-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
